LONDON — Prime Minister Boris Johnson faced a torrent of calls on Saturday to dismiss his most influential adviser, Dominic Cummings, after reports that Mr. Cummings had visited relatives in northern England while he was ill with the coronavirus — a violation of Britain’s lockdown rules.

Mr. Johnson appeared determined to stand by Mr. Cummings, an enigmatic figure who helped mastermind his election victory last year and the Brexit campaign that resulted in Britain’s departure from the European Union.

But the reports that Mr. Cummings had driven to his parents’ house in Durham in April when the government was urging people to stay home — particularly those with symptoms of the virus — set off a political tempest, with critics accusing him of flouting the rules that apply to everybody else.

“The British people do not expect there to be one rule for them and another rule for Dominic Cummings,” said a spokesman for the opposition Labour Party, who added that he had “breached the lockdown rules.”

Leaders of two other opposition parties, the Liberal Democrats and Scottish National Party, demanded that he resign or be fired.

Confronted by reporters outside his home on Saturday, Mr. Cummings said, “I behaved reasonably and legally.” Asked whether his decision had been “a good look,” he replied: “Who cares about good looks? It’s a question of doing the right thing. It is not about what you guys think.”

The furious reactions to his trip attested to the polarizing role Mr. Cummings has played in British politics since before the 2016 Brexit referendum. He has accumulated a long list of enemies, including some in the Conservative Party, like Iain Duncan Smith, a former party leader, whom he has ridiculed or sidelined.

But it also showed Mr. Johnson’s deep reliance on Mr. Cummings. The prime minister dug in his heels on Saturday, releasing a statement, through a spokesman, that defended Mr. Cummings and his wife for making the 260-mile drive to Durham. t said, they had been trying to line up care for their young child after he contracted the virus and expected he would fall ill.

The adviser went to a house “near to but separate from his extended family,” the statement said, after his sister and nieces had offered to help.

“His actions were in line with coronavirus guidelines,” the statement said.

But Robert Jenrick, the secretary for housing, communities and local government, held on to his job after admitting he had driven an hour outside London to visit his parents. And Stephen Kinnock, a prominent Labour member of Parliament, brushed aside criticism from the police after he visited his father, Neil Kinnock, for his birthday in March.

His public profile rose when he was portrayed by the actor Benedict Cumberbatch in a drama about the Brexit campaign, as a sort of tortured genius determined to destroy the political elite. Since the election, he has reveled in his image as an eccentric, disheveled iconoclast, intent on reinventing government — Downing Street’s answer to Stephen K. Bannon, President Trump’s former strategist.

Cabinet ministers and other Conservative lawmakers showed support for Mr. Cummings on Saturday, including the foreign secretary, Dominic Raab; the chancellor of the Exchequer, Rishi Sunak; and the health secretary, Matt Hancock.

“I know how ill coronavirus makes you,” Mr. Hancock tweeted. “It was entirely right for Dom Cummings to find childcare for his toddler, when both he and his wife were getting ill.”

Others stayed silent, however, perhaps waiting to see whether Mr. Cummings could ride out the storm.

While the Labour Party demanded answers, it stopped short of demanding his resignation. That appeared to reflect a tactical judgment by the party leader, Keir Starmer, that the episode would do more damage to the government, which is already on the defensive for its handling of the virus, if it were dragged out over several days.

And criticism flowed not just from opposition politicians.

Julia Hartley-Brewer, a broadcaster and journalist who generally leans to the right politically, described how she had been separated from her 77-year-old mother, who lives on her own and suffered a heart attack in December.